Updated 12 October 2026 · By Pete Bromfield, former Head of Maths with IB examining experience

Is Moore's law still true?

AA SLAI SLAA HLAI HL Accessible Also in: Statistics

Research question

Has the number of transistors on microprocessors doubled every two years since 1971, and is there evidence that the doubling time has changed?

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Why it makes a good exploration

Moore's law is quoted everywhere, usually without checking. Fitting an exponential model, extracting the doubling time and testing whether it has changed over different decades is a precise, answerable question.

The mathematics you'll need

Exponential models and doubling time
Logarithms to linearise data
Linear regression on log-transformed data
Comparing gradients across time periods

Modelling the data, step by step

This idea usually needs exponential or straight-line models. See it worked step by step, with a criterion tip at every step: Exponential y = a e^(kx) + c and y = a·bˣ · Straight line y = mx + c.

Model your own data Paste it from Desmos, GeoGebra or a spreadsheet and get the same play-by-play with your numbers. New to modelling? Start with the modelling workflow. Writing it up? The IA modelling planner comments on each paragraph as you draft — it never writes it for you.

Where the data comes from

Download the “transistors per microprocessor” dataset from Our World in Data.

Real data for this idea

Primary source: Karl Rupp, microprocessor trend data: Microprocessor trend data. The transistors file gives year and transistor count per chip: fit log(count) against year. Licence: Check the repository's licence file.
Readable chart: Our World in Data: Moore's law: The number of transistors per microprocessor. Use it to see the pattern; download your numbers from the primary source or the chart's own download. Cite as: Our World in Data, ‘Moore's law: The number of transistors per microprocessor’, CC BY 4.0. Original source: Rupp (2022).

Links checked October 2026; we link to the data and never copy it. More free data sets.

A possible outline

State Moore's claim precisely (doubling every two years).
Plot log₂ of transistor count against year.
Fit a line and convert the gradient to a doubling time.
Fit separate lines to each decade and compare doubling times.
Discuss what the log scale hides and what limits further growth.

Pitfalls that cost marks

Fitting y = abˣ without explaining the log transformation.
Treating the dataset as one chip per year (it is a scatter of chips).
Not checking residuals on the log scale.

Showing personal engagement

Predict the transistor count of the processor in your own phone or laptop and look it up.
Discuss whether a slowdown is visible and propose a model that captures it.
Compare with another exponential claim in technology.

See Criterion C: personal engagement for what examiners look for.

Which course is it for?

Course	Fit	Maths to lean on
AA SL	Good fit	Exponential models and doubling time; Logarithms to linearise data
AA HL	Fits, but add an HL technique	Exponential models and doubling time; Logarithms to linearise data
AI SL	Good fit	Exponential models and doubling time; Logarithms to linearise data
AI HL	Fits, but add an HL technique	Exponential models and doubling time; Logarithms to linearise data

Level: Accessible. A good first extended piece of maths, with room to go deeper. See how the IA differs between AA and AI, SL and HL.

How this idea reaches the top bands

Reflection (D)

For this idea, start with the weak points: fitting y = abˣ without explaining the log transformation; and treating the dataset as one chip per year (it is a scatter of chips). Say how each one affects your answer.

Use of mathematics (E)

SL: exponential models and doubling time; logarithms to linearise data; linear regression on log-transformed data; comparing gradients across time periods, each explained in your own words and carried out correctly.

How modelling explorations reach the top bands in general: Modelling with functions IA ideas. Guides: A · B · C · D · E · self-grade sheet.

Taking it further

Test whether a logistic or piecewise model fits significantly better, or compare with the growth of hard-drive capacity.

Extending it for HL

Add an HL technique the question genuinely needs: what an HL modelling exploration adds.

See a complete IA, marked

Should I lease or buy my first car? (AI SL) is a complete modelling exploration, marked on every criterion.

Frequently asked questions

Which IB Maths course is this IA idea for?

It works for AA SL, AI SL, AA HL and AI HL. We rate it Accessible: a good first extended piece of maths, with room to go deeper.

What mathematics does this IA use?

Exponential models and doubling time, logarithms to linearise data, linear regression on log-transformed data and comparing gradients across time periods.

Where can I get data for this IA?

Download the “transistors per microprocessor” dataset from Our World in Data. Checked sources and tools: Karl Rupp, microprocessor trend data and Our World in Data.

Turn this idea into your IA

The planner opens with “Is Moore's law still true?” filled in: the question, the maths and the data sources.

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